Question: Find the distance between the points (-5, 6) and (-6, -6). ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-5, 6)$ $(-6, -6)$ $1$ $12$
Change in $x$ -5 (-6) Change in $y$ (-6) 12 The distance is the length of the hypotenuse of this right triangle. By the Pythagorean Theorem, that length is equal to: $\sqrt{1^2 + 12^2}$ $= \sqrt{145}$